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$1,000 is invested in an account where the interest is compounded monthly at a 6% nominal annual interest rate. If $15 is withdrawn at the end of each month, how much money remains in the account after five years (on the date of the 60th withdrawal)?

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Jarrod Robel
Jarrod RobelLv2
28 Sep 2019

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it's about Compound Interest Future Value

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Assume the interest rate on a savings account pays 7 percent annual interest.

1-If the interest is compounded annually, what is the future value of $1,000 invested in this account for 6 years?

2-If the interest is compounded monthly, what is the future value of $1,000 invested in this account for 6 years?

3-If the interest is compounded daily, what is the future value of $1,000 invested in this account for 6 years?

Q1. Suppose you deposit fund in a bank saving account each month as follows:

- For the first twenty months, the deposits are $1,000 per month deposited at the end of each month. - The first deposit takes place at the end of the first month. - For the 21st till the 40th month, the deposited amounts increase by $10 from previous month deposit. Still, deposits are made at the end of each month. -For example, the deposit in the 21st month is $1,000+$10 = $1,010. - For the 41st till the 60th month, the deposits increase by 2% each month as compared to the previous year. Still, deposits are made at the end of each month. -For example, the deposit at the end of the 41st month is: (1,000+10*20) * (1+0.02) = $1,224. -Subsequently, the deposit at the end of the 42nd month is: (1,000+10*20) * (1+0.02)2 = $1248.48. The saving account is expected to have an interest at a rate of 0.35% per month. Assume that you don’t withdraw the interest earned at the end of each interest period (year), but instead let it accumulate.

a] How much will you have at the end of the 60th month? Please note that compounding is monthly as stated earlier. b] Now suppose that all payments made by you remain the same but another bank is offering the following information to attract your business: - Compounding is daily - Nominal annual interest rate is 4.1% Calculate how much you are expected to have at the end of the 60th month given this new information. Note: In this question, you are expected to use compounding factors for uniform, arithmetic, and geometric series. Please show clearly your calculations steps.

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